Goal
Write a decoder to allow the rebellion to decipher the Empire's secret messages.
The rebelllion figured out that characters in the original message are encoded by XOR'ing them with a stream of random numbers:
- The Empire uses ASCII codes for their original message.
- First character of each original message is always @.
- Each message is encoded with a different Seed for the Random Number Generator (RNG).
- The first Offset numbers from the RNG are discarded before encoding.
- Each undiscarded random number from the RNG is then XOR'ed with the ASCII code of each character, truncated to the lowest 8 bits. The resulting number then becomes part of the encoded message.
- The RNG used is:
R(n+1) = (7562100 * R(n) + 907598307) mod 7140
where R(0) = Seed, R(1) is the first number from the RNG, R(2) is the second, etc.
The Empire believes that security is guaranteed by using large seeds (0 < Seed < 2^63) and the large offsets ( 0 ≤ Offset < 2^63) which should prevent any brute force attack. Apparently you have a better way to work around the security than simple brute force!
Example
The original message @Hello is encoded with Seed = 581980637 and Offset = 10 to obtain the encoded message of 135 155 214 19 183 44.
Input
Line 1: An integer Offset for the random numbers from the RNG to discard before starting XOR'ing.
Line 2: An integer Length for the length of the message including @.
Next Length lines: One integer C in each line for each encoded character of the message.
Output
Line 1: The decoded message excluding the initial @.
Constraints
0 < Seed < 2^63
0 ≤ Offset < 2^63
0 < Length < 256
32 ≤ ASCII code of each character in the original message ≤ 126
Example
Input
10
6
135
155
214
19
183
44
